Spun multicore fiber has been used to determine the shape of an optical fiber. A multicore fiber having four cores can be used to separate the deformation of the fiber into two bend angles (pitch and yaw), one twist angle, and the fiber elongation. These four measurements constitute four degrees of freedom. These four measurements (pitch, yaw, twist, and elongation) also represent all of the deformations that can happen to the fiber with relatively small forces.
In fiber optic based shape sensing, a multi-channel distributed strain sensing system is used to detect the change in strain for each of several cores within a multicore optical shape sensing fiber as described in U.S. Pat. No. 8,773,650, incorporated herein by reference. Multiple distributed strain measurements are combined through a system of equations to produce a set of physical measurements including curvature, twist, and axial strain as described in U.S. Pat. No. 8,531,655, incorporated herein by reference. These physical measurements can be used to determine the distributed shape and position of the optical fiber. Temperature can also change the apparent length of the cores and represents a fifth degree of “freedom” in the system. The shape sensing systems described in the above patents do not distinguish between temperature changes along the length of the fiber and axial strain changes along the length of the fiber.